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Functional Analysis Valencia 2000
July 3-7, 2000
Technical University of Valencia (UPV) and University of Valencia (UV)
Valencia, Spain

Organizers
R.M. Aron (Kent State U., USA), K.D. Bierstedt (U. Paderborn, Germany), J. Bonet (UPV), J. Cerdà (U. Barcelona, Spain), H. Jarchow (U. Zürich, Switzerland), M. Maestre (UV), J. Schmets (U. Liège, Belgium)

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Feynman's operational calculus for an operator-valued function space integral
by
Kun Soo Chang
Yonsei University
Coauthors: K.P. Hong (Daelim University), K.S. Ryu (Hannam University)

In this paper, we study Feynman's operational calculus and change of scale for the sequential operator-valued function space integral as a bounded linear operator from L2(R) into itself. In fact, we define multiplication (*) and addition (+) operators on functionals defined on the space of all piecewise continuous functions on [0, t] and give algebraic properties of the operators. We show that the sequential operator- valued function space integral of F*G is the product of the integrals of F and G. Also the integral of exp(F+G) is the product of the integrals of exp(F) and exp(G). Then we show that the integral of the commutator of F and G is the commutator of the integrals of F and G. Finally, we give a formula for change of scale for the integral.

(T)

Date received: April 3, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caei-61.